Rewriting rule methods in logic databases

We consider proposals rewriting a set of Horn clauses (originally conceived for a backward, Prolog-like , evaluation) into another set of clauses that can be efficiently executed using a forward strategy. In particular, we cocnentrate on the Counting and on the Alexander methods. For both of them, we assume the forward evaluation strategy defined for the Alexander approach based on the saturation (of a set of clauses) operator. Under this hypothesis, the two rewriting methods are compared with the original logic environment by means of a stack machine, which is used as a refernce environment for our comparison.